Tension in Vertical Circular Motion at Lowest Point – Rankers Physics

Vertical Circular Motion: Practice Problem & Solution

A point mass '$m$' is moved in a vertical circle of radius '$r$' with the help of a string. The velocity of the mass is $\sqrt{7gr}$ at the lowest point. The tension in the string at the lowest point is (2020-Covid)
$7 \text{ mg}$
$8 \text{ mg}$
$1 \text{ mg}$
$6 \text{ mg}$

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Vertical Circular Motion. Understanding the underlying formula is key to arriving at the correct answer below:

Tension at the lowest point is given by $T = mg + \frac{mv^2}{r} = mg + \frac{m(\sqrt{7gr})^2}{r} = mg + 7mg = 8mg$.

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